A Brisk Estimator for the Angular Multipoles (BEAM) of the redshift space bispectrum

TL;DR

This paper introduces a fast FFT-based estimator for computing angular multipoles of the redshift space bispectrum, significantly reducing computational time and capturing rich cosmological information from large-scale structure data.

Contribution

It presents a novel, efficient method to estimate all bispectrum multipoles including m≠0, improving upon traditional computational approaches.

Findings

Estimator accurately recovers all bispectrum multipoles up to ℓ=6, m=6.

Validation against analytical results shows high agreement.

Method reduces computation time from O(Ng^6) to O(Ng^4).

Abstract

The anisotropy of the redshift space bispectrum depends upon the orientation of the triangles formed by three $\vec{k}$ modes with respect to the line of sight. For a triangle of fixed size ($k_1$) and shape ($\mu,t$), this orientation dependence can be quantified in terms of angular multipoles $B_\ell^m(k_1,\mu,t)$ which contain a wealth of cosmological information. We propose a fast and efficient FFT-based estimator that computes the bispectrum multipole moments $B_\ell^m$ of a 3D cosmological field for all possible $\ell$ and $m$ (including $m\neq 0$). The time required by the estimator to compute all multipoles from a gridded data cube of volume $N_g^3$ scales as $\sim \mathcal{O}(N_g^4)$ in contrast to the direct computation technique which requires time $\sim \mathcal{O}(N_g^6)$. Here, we demonstrate the formalism and validate the estimator using a simulated non-Gaussian field for which the analytical expressions for all the bispectrum multipoles are known. The estimated results are found to be in good agreement with the analytical predictions for all $16$ non-zero multipoles (up to $\ell= 6, m=6$). We expect the $m \neq 0$ bispectrum multipoles to significantly enhance the information available from galaxy redshift surveys and future redshifted 21-cm observations.